Initiates, Magic, and Strain I infected

Being a Strain I Infected means that your essence and therefore Magic rating will be in constant flux. As you lose essence you lose magic as usual. However as an Strain I infected you can regain lost magic by draining essence. I have two questions in this regard:

1: in order to “regain” a lost point you have to have paid for it fully in the first place, right? Say a magician becomes a rank 1 initiate they new maximum would be 7. However this seventh point can only be considered lost once the magician has paid 35 karma points for it, correct?

2: the maximum essence rating needed in order to start converting essence drained into magic is 12 (minus implants etc.) correct? Not 6?

Looking at rules for Magic and Essence in Run Faster (p.141). A vampire's maximum Magic attribute is their current Essence plus their Initiate Grade. If they let their Essence drop too low, they start losing points of Magic.

Say a vampire magician (not an initiate) with Magic 6 gets a little careless about his Essence, and lets it fall to Essence 5. By the rules in Run Faster, he also loses a point of Magic. Once he finds a victim to drain and replenishes his Essence, the point of Magic doesn't come back automatically. He has to "reconnect" the lost point by taking a geas, by draining extra Essence (beyond the limit of 12), or by spending 6 karma (only 1x the restored level, not 5x as if he were raising the attribute for the first time). Draining extra Essence seems the obvious best option, but it does trigger an addiction test.

Now, say a vampire grade-1 initiate spends 35 karma to raise his Magic Attribute to 7. Same situation. When his Essence drops down to 5, his Magic falls to 6 (max is current Essence plus Initiate Grade). After he refills his Essence tank, he can recover the lost point of Magic by any of the same three methods (geas, surplus Essence, or 7 karma).